(1/[alpha])-Self similar [alpha]-stable processes with stationary increments

In this note we settle a question posed by Kasahara, Maejima, and Vervaat. We show that the [alpha]-stable Lévy motion is the only (1/[alpha])-self-similar [alpha]-stable process with stationary increments if 0 < [alpha] < 1. We also introduce new classes of (1/[alpha])-self-similar [alpha]-stable processes with stationary increments for 1 < [alpha] < 2.

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Year of publication:	1990
Authors:	Samorodnitsky, Gennady ; Taqqu, Murad S.
Published in:	Journal of Multivariate Analysis. - Elsevier, ISSN 0047-259X. - Vol. 35.1990, 2, p. 308-313
Publisher:	Elsevier
Keywords:	stable distributions self-similar processes stable Lévy motion

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Type of publication:	Article
Source:	RePEc - Research Papers in Economics

Persistent link: https://www.econbiz.de/10005006487